287 lines
8.0 KiB
C++
287 lines
8.0 KiB
C++
// Copyright (c) 2000
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h $
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// $Id: Sphere_3.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Herve Bronnimann
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#ifndef CGAL_CARTESIAN_SPHERE_3_H
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#define CGAL_CARTESIAN_SPHERE_3_H
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#include <CGAL/Handle_for.h>
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#include <CGAL/Interval_nt.h>
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#include <boost/tuple/tuple.hpp>
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#include <CGAL/Kernel/global_functions_3.h>
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namespace CGAL {
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template <class R_>
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class SphereC3
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{
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typedef typename R_::FT FT;
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// https://doc.cgal.org/latest/Manual/devman_code_format.html#secprogramming_conventions
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typedef typename R_::Point_3 Point_3_;
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typedef typename R_::Vector_3 Vector_3;
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typedef typename R_::Sphere_3 Sphere_3;
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typedef typename R_::Circle_3 Circle_3;
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typedef boost::tuple<Point_3_, FT, Orientation> Rep;
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typedef typename R_::template Handle<Rep>::type Base;
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Base base;
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public:
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typedef R_ R;
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SphereC3() {}
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SphereC3(const Point_3_ ¢er, const FT &squared_radius,
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const Orientation &o = COUNTERCLOCKWISE)
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{
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CGAL_kernel_precondition( (squared_radius >= FT(0)) &
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(o != COLLINEAR) );
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base = Rep(center, squared_radius, o);
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}
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// Sphere passing through and oriented by p,q,r,s
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SphereC3(const Point_3_ &p, const Point_3_ &q,
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const Point_3_ &r, const Point_3_ &s)
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{
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Orientation orient = make_certain(CGAL::orientation(p, q, r, s));
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Point_3_ center = CGAL::circumcenter(p, q, r, s);
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FT squared_radius = squared_distance(p, center);
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base = Rep(center, squared_radius, orient);
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}
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// Sphere with great circle passing through p,q,r, oriented by o
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SphereC3(const Point_3_ &p, const Point_3_ &q, const Point_3_ &r,
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const Orientation &o = COUNTERCLOCKWISE)
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{
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CGAL_kernel_precondition(o != COLLINEAR);
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Point_3_ center = CGAL::circumcenter(p, q, r);
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FT squared_radius = squared_distance(p, center);
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base = Rep(center, squared_radius, o);
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}
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// Sphere with diameter pq and orientation o
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SphereC3(const Point_3_ &p, const Point_3_ &q,
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const Orientation &o = COUNTERCLOCKWISE)
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{
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CGAL_kernel_precondition(o != COLLINEAR);
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Point_3_ center = midpoint(p, q);
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FT squared_radius = squared_distance(p, center);
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base = Rep(center, squared_radius, o);
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}
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explicit SphereC3(const Point_3_ ¢er,
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const Orientation& o = COUNTERCLOCKWISE)
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{
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CGAL_kernel_precondition(o != COLLINEAR);
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base = Rep(center, FT(0), o);
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}
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typename R::Boolean operator==(const SphereC3 &) const;
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typename R::Boolean operator!=(const SphereC3 &) const;
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const Point_3_ & center() const
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{
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return get_pointee_or_identity(base).template get<0>();
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}
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const FT & squared_radius() const
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{
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// Returns the square of the radius (instead of the radius itself,
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// which would require square roots)
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return get_pointee_or_identity(base).template get<1>();
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}
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Orientation orientation() const
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{
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return get_pointee_or_identity(base).template get<2>();
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}
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// A circle is degenerate if its (squared) radius is null or negative
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typename R::Boolean is_degenerate() const;
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// Returns a circle with opposite orientation
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Sphere_3 opposite() const;
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typename R_::Oriented_side oriented_side(const Point_3_ &p) const;
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//! precond: ! x.is_degenerate() (when available)
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// Returns R::ON_POSITIVE_SIDE, R::ON_ORIENTED_BOUNDARY or
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// R::ON_NEGATIVE_SIDE
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typename R::Boolean has_on(const Circle_3 &p) const;
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typename R::Boolean has_on(const Point_3_ &p) const;
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typename R::Boolean has_on_boundary(const Point_3_ &p) const;
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typename R::Boolean has_on_positive_side(const Point_3_ &p) const;
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typename R::Boolean has_on_negative_side(const Point_3_ &p) const;
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typename R_::Bounded_side bounded_side(const Point_3_ &p) const;
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//! precond: ! x.is_degenerate() (when available)
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// Returns R::ON_BOUNDED_SIDE, R::ON_BOUNDARY or R::ON_UNBOUNDED_SIDE
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typename R::Boolean has_on_bounded_side(const Point_3_ &p) const;
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typename R::Boolean has_on_unbounded_side(const Point_3_ &p) const;
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};
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template < class R >
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CGAL_KERNEL_INLINE
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typename R::Boolean
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SphereC3<R>::operator==(const SphereC3<R> &t) const
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{
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if (CGAL::identical(base, t.base))
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return true;
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return center() == t.center() &&
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squared_radius() == t.squared_radius() &&
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orientation() == t.orientation();
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::operator!=(const SphereC3<R> &t) const
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{
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return !(*this == t);
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}
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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typename R::Oriented_side
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SphereC3<R>::
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oriented_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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return enum_cast<Oriented_side>(bounded_side(p)) * orientation();
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}
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template < class R >
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CGAL_KERNEL_INLINE
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typename R::Bounded_side
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SphereC3<R>::
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bounded_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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return enum_cast<Bounded_side>(compare(squared_radius(),
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squared_distance(center(), p)));
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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has_on(const typename SphereC3<R>::Circle_3 &c) const
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{
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typedef typename SphereC3<R>::Point_3_ Point_3_;
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typedef typename SphereC3<R>::FT FT;
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Point_3_ proj = c.supporting_plane().projection(center());
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if(!(proj == c.center())) return false;
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const FT d2 = squared_distance(center(),c.center());
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return ((squared_radius() - d2) == c.squared_radius());
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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has_on(const typename SphereC3<R>::Point_3_ &p) const
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{
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return has_on_boundary(p);
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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has_on_boundary(const typename SphereC3<R>::Point_3_ &p) const
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{
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// FIXME: it's a predicate...
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return squared_distance(center(),p) == squared_radius();
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// NB: J'ai aussi trouve ailleurs :
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// return oriented_side(p)==ON_ORIENTED_BOUNDARY;
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// a voir...
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}
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template < class R >
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CGAL_KERNEL_INLINE
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typename R::Boolean
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SphereC3<R>::
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has_on_negative_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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if (orientation() == COUNTERCLOCKWISE)
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return has_on_unbounded_side(p);
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return has_on_bounded_side(p);
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// NB: J'ai aussi trouve ailleurs :
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// return oriented_side(p)==ON_NEGATIVE_SIDE;
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}
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template < class R >
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CGAL_KERNEL_INLINE
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typename R::Boolean
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SphereC3<R>::
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has_on_positive_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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if (orientation() == COUNTERCLOCKWISE)
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return has_on_bounded_side(p);
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return has_on_unbounded_side(p);
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// NB: J'ai aussi trouve ailleurs :
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// return oriented_side(p)==ON_POSITIVE_SIDE;
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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has_on_bounded_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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// FIXME: it's a predicate...
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return squared_distance(center(),p) < squared_radius();
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// NB: J'ai aussi trouve ailleurs :
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// return bounded_side(p)==ON_BOUNDED_SIDE;
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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has_on_unbounded_side(const typename SphereC3<R>::Point_3_ &p) const
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{
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// FIXME: it's a predicate...
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return squared_distance(center(),p) > squared_radius();
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// NB: J'ai aussi trouve ailleurs :
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// return bounded_side(p)==ON_UNBOUNDED_SIDE;
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}
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template < class R >
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inline
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typename R::Boolean
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SphereC3<R>::
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is_degenerate() const
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{
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// FIXME: it's a predicate (?)
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return CGAL_NTS is_zero(squared_radius());
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}
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template < class R >
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inline
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typename SphereC3<R>::Sphere_3
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SphereC3<R>::opposite() const
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{
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return SphereC3<R>(center(), squared_radius(),
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CGAL::opposite(orientation()) );
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}
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} //namespace CGAL
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#endif // CGAL_CARTESIAN_SPHERE_3_H
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